Question

How do you convert $325{}^\circ $ to radians?

Answer 1

Hint: Here we have to convert radian to degree, we have degrees $=$ radian $\times \dfrac{180{}^\circ }{\pi }$
Further converting degree to radians
Radians $=$ degrees $\times \dfrac{\pi }{180{}^\circ }$

Complete step-by-step answer:
In the above question we have to convert degrees into radians.
Let us consider a circle and an angle if suppose the arc cut that angle is equal to its radius.
Then if we are going to measure the angle it will be $1$ radian.
If the angle cut the circle i.e. angle cut the circle two times we will consider it as $2$ radian.
Here, the circumference of the circle when we consider it is equal to radius. Then the angle of $360{}^\circ $ is considered as $2\pi $ is considered as $2\pi $ radians.
As we know that $360{}^\circ =2\pi $ radians.
So, we are considering $1{}^\circ $
Thus we are finding the radian for $1{}^\circ $ will be,
$1{}^\circ $ is equal to $\dfrac{2\pi }{360}$ radians.
$1{}^\circ =\dfrac{2\pi }{360}$ radians.
So, now we have to find out the value for $325{}^\circ $
Thus multiplying with $325{}^\circ $ we get,
$325{}^\circ =\dfrac{2\pi }{360}325$ radians.
Substituting the value of $\pi $ as $3.1416$
We have
$=\dfrac{2\times 3.1416\times 325}{360}$
So, after multiplying we get,
$5.6723$ radians.

Hence after converting $325{}^\circ $ in radian is $5.6723$ radian.

Additional Information:
Considering the conversion table from degree to radians.
$0{}^\circ $ is equal to $0$ radian
$30{}^\circ $ is equal to $\dfrac{\pi }{6}$ radian
$45{}^\circ $ is equal to $\dfrac{\pi }{4}$ radian
$60{}^\circ $ is equal to $\dfrac{\pi }{3}$ radian
$90{}^\circ $ is equal to $\dfrac{\pi }{2}$ radian
$120{}^\circ $ is equal to $\dfrac{2\pi }{3}$ radian
$135{}^\circ $ is equal to $\dfrac{3\pi }{4}$ radian
$150{}^\circ $ is equal to $\dfrac{5\pi }{6}$ radian
$180{}^\circ $ is equal to $\pi $ radian
$270{}^\circ $ is equal to $\dfrac{3\pi }{2}$ radian
$360{}^\circ $ is equal to $2\pi $ radian.
Thus above is the degree conversion.

Note:
While we are converting from degree to radian we have to be careful regarding formula.
Pi radians are equal to $180$ degrees.
i.e. $\pi\ rad=180{}^\circ $
one degree is equal to $0.01745329252$ radian.